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A Solution of Gaussian Optimizer Conjecture for Quantum Channels

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Abstract

The long-standing conjectures of the optimality of Gaussian inputs and additivity are solved for a broad class of gauge-covariant or contravariant bosonic Gaussian channels (which includes in particular thermal, additive classical noise, and amplifier channels) restricting to the class of states with finite second moments. We show that the vacuum is the input state which minimizes the entropy at the output of such channels. This allows us to show also that the classical capacity of these channels (under the input energy constraint) is additive and is achieved by Gaussian encodings.

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Authors and Affiliations

  1. NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, 56127, Pisa, Italy

    V. Giovannetti

  2. Steklov Mathematical Institute, RAS, 119991, Moscow, Russia

    A. S. Holevo

  3. National Research University Higher School of Economics (HSE), 101000, Moscow, Russia

    A. S. Holevo

  4. Center for Quantum Information and Communication, Ecole Polytechnique de Bruxelles, CP 165, Universite Libre de Bruxelles, 1050, Bruxelles, Belgium

    R. García-Patrón

  5. Max-Planck Institut für Quantenoptik, Hans-Kopfermann Str. 1, 85748, Garching, Germany

    R. García-Patrón

Authors
  1. V. Giovannetti
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  2. A. S. Holevo
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  3. R. García-Patrón
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Corresponding author

Correspondence to A. S. Holevo.

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Communicated by M. M. Wolf

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Giovannetti, V., Holevo, A.S. & García-Patrón, R. A Solution of Gaussian Optimizer Conjecture for Quantum Channels. Commun. Math. Phys. 334, 1553–1571 (2015). https://doi.org/10.1007/s00220-014-2150-6

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  • DOI: https://doi.org/10.1007/s00220-014-2150-6

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